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Whitepunk [10]
4 years ago
8

Show that A x B does not equal B x A, when A and B are nonempty unless A=B.

Mathematics
1 answer:
Shtirlitz [24]4 years ago
8 0
We will assume A×B = B×A and show that A and B are necessarily the same.

Assume A×B = B×A. Let a ∈ A and b ∈ B. Then (a,b) ∈ A×B. Since A×B = B×A, we have (a,b) ∈ B×A. That is, a ∈ B and b ∈ A. Therefore, a ∈ A implies a ∈ B and b ∈ B implies b ∈ A. So A = B, as we had set out to do.
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